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Anonymous Poster #1

Dimensional Analysis Question Help

10/17/2017 6:36 AM

I've been given this question to do and I'm abit stuck.


For a, I substituted in the dimensions into the equation and see what it gave me. I got m^3 (Working out attached). Is this the right method?

What exactly does dimensionally sound mean?

for part b) I just made y the subject by taking EI to the other side, subbing in the numbers and inputting it into a calculator....


I have a feeling this is completely wrong.

What method do I use?

Sorry for my incompetence -_-'

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#1

Re: Dimensional Analysis Question Help

10/17/2017 9:37 AM

Pay careful attention to units.

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#2
In reply to #1

Re: Dimensional Analysis Question Help

10/17/2017 9:46 AM

For part b?

Have I done part a correctly?

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#11
In reply to #2

Re: Dimensional Analysis Question Help

10/18/2017 11:37 AM

Part 'a' you have gotten to where you should, though your description of the path you took could be a little more clear/explicit than detailed on the ruled paper.

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#12
In reply to #2

Re: Dimensional Analysis Question Help

10/18/2017 11:46 AM

Part a) has been covered by other posts.

For part b) I suspect it's meant to encourage you to check units. Apart from 3 length units, you've got GPa and kN. BTW, q should be in kN/length, not kN, and kN/m gives a reasonable distributed load.

There's other things wrong. I assume it's just an academic exercise, and material isn't mentioned, but for steel (which beams are usually made of!) E is about 220GPa, not 22.

Also formula (2) is wrong. You can see that because y must = 0 when x = 0 and when x = L. It should be (y +ve downwards)

or better

With E = 220GPa, and using Mathcad, which takes care of the units for you, I make y = 55mm. Clearly much too high for a practical application.

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#13
In reply to #12

Re: Dimensional Analysis Question Help

10/19/2017 1:10 PM

My rusty math can just about keep up with your approach, but as you say, E is a bit on the high side - by a magnitude of 10 - and I guess intentional judging by the way the question is presented - (it hints of 'trickery' to catch out the unaware) - together with the answer for deflection to be given in meters - whereas the distance to the deflection is given cm, and the overall length between supports is given in mm.

A little trick I learned very early on in slide-rule days dealing with real situations, is to do the 'sums' to get the 'numbers', then use common sense to 'guesstimate' where the decimal point should go in the answer. Then double check if it seems wrong.

Although in the question as put, the deflection if stated in metres, would have leading decimal places and zeros to confuse me.

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#3

Re: Dimensional Analysis Question Help

10/17/2017 10:08 AM

Dimensionally sound means that the dimensions on the left side of the equation should be the same as the dimensions on the right.

Take the left side:

y = distance = meters

dy/dx = distance/distance = unitless

dy2/dx2 = distance/distance2 = m-1

dy3/dx3 = m-2

dy4/dx4 = m-3

Right side: q(x)/E*I = (N/m) /(( N/m2)(m4)) = (N/m)/(Nm2) = m-3

Always do your calculations with units, and verify the answer has the right units.

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#4
In reply to #3

Re: Dimensional Analysis Question Help

10/17/2017 10:22 AM

Your derivative notation is incorrect.

You meant the second, third, and fourth derivatives of y, not the derivatives of y2, y3, and y4.

I.e., you meant to write d2y/dx2, d3y/dx3, d4y/dx4.

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#8
In reply to #4

Re: Dimensional Analysis Question Help

10/17/2017 1:51 PM

You're right, thanks!

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#5
In reply to #3

Re: Dimensional Analysis Question Help

10/17/2017 12:34 PM

"dy2/dx2 = distance/distance2 = m-1"

if dy has units of meters wouldn't dy2 have units of m2 ?

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#9
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Re: Dimensional Analysis Question Help

10/17/2017 1:55 PM

Yup, got the little numbers in the wrong place. Sorry. See #8.

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#6

Re: Dimensional Analysis Question Help

10/17/2017 12:50 PM
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#7
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Re: Dimensional Analysis Question Help

10/17/2017 1:36 PM

Clear as mud.

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#10

Re: Dimensional Analysis Question Help

10/18/2017 6:28 AM

You have been given dimensions in mm, cm and m.

The answer (the deflection) is to be given in metres, whereas the distance from the end is stated in cm.

You have to makes sure that all lengths in the equation use the same units matched to those in Young's Modulus�.

At the same time, you need to make sure 'dimensional relationships' in the given formula are correct.

I am too rusty on maths to say, but it is a bit sneaky if they are not

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